The theory of slow acoustic modes propagating along the optical fiber and being controlled by the nanoscale variation of the effective fiber radius (analogous to the theory of slow optical whispering gallery modes) is developed. Surprisingly, it is shown that, in addition to acoustic bottle resonators (which are similar to optical bottle resonators), there exist antibottle resonators, the neck-shaped deformations of the fiber that can fully confine acoustic modes. It is also shown that an eigenfrequency of the mechanical vibrations of a silica parabolic bottle resonator can match the separation between the eigenfrequencies of a series of its optical modes, thereby enabling the resonant mechanical excitation of these series. The developed theory paves the groundwork for slow-mode optomechanics in an optical fiber.
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